FreeBSD would be a useful choice because of the support for filesystem snapshots. It's stable and I believe all of the components Zimbra needs are available now.
Snapshots are handy way of getting backups for FOSS users:
$ zmcontrol stop
$ mount -o snapmount -u ...
$ zmcontrol start
would result in only a few seconds of down time. FreeBSD's UFS2 has supported snapshots for quite some time, and FreeBSD supports ZFS too.